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此内容主要针对于吴恩达的神经网络与深度学习课后作业(第一课第二周的作业)进行学习,记录。

参考连接https://github.com/andersy005/deep-learning-specialization-coursera

说明

实现功能:这段代码主要实现的功能是判断一张图片是否有cat,实现的是二分类,有就为1,没有就为0。

训练方法:BP网络,此代码很简单,没有隐藏层,直接就是输入层连着输出层,z=W\'X+b,a=sigmoid(z) ,y=a故权值w是一维。(这一步体现在initialiize_with_zeros()中第21行)网络结构如下图所示:(实际输入不止x1,x2,x3。是x1,x2~~x12288.(个数是由图片64*64*3算出来的))

难点说明: 第34行:dw = (1./m)*np.dot(X,((A-Y).T))     此处的dw是指(dL/dw),即损失函数对权值w的导数,此公式是由微积分的链式求导法则推导出来的,吴恩达视频里有,不清楚的请看视频。(2.9 logistic回归中的梯度下降法),这里如果理解了,整个代码也没啥难度了。

 

BP算法

 

基本思想:学习过程由信号的正向传播和误差的反向传播两个过程组成。(这一步体现在propagate()函数)

 

数学工具:微积分的链式求导法则。(这一步体现在propagate()函数中第34行)

 

求解最小化成本函数(cost function):梯度下降法。(这一步体现在optimize()函数)

 

注意

1.损失函数和代价函数的区别:

损失函数(Loss function):指单个训练样本进行预测的结果与实际结果的误差。

代价函数(Cost function):整个训练集,所有样本误差总和(所有损失函数总和)的平均值。(这一步体现在propagate()函数中的第32行)

  1 #!/usr/bin/env python3
  2 # -*- coding: utf-8 
  3 
  4 import numpy as np
  5 import matplotlib.pyplot as plt
  6 import h5py
  7 import scipy
  8 from PIL import Image
  9 from scipy import ndimage
 10 from lr_utils import load_dataset
 11 import pylab
 12 
 13 #sigmoid函数
 14 def sigmoid(z):
 15     s = 1./(1+np.exp(-z))
 16     return(s)
 17 
 18 #初始化权值阈值
 19 def initialiize_with_zeros(dim):
 20     #这里只有一个神经元,w是一维的
 21     w = np.zeros(shape = (dim,1), dtype = np.float32)
 22     b = 0
 23     #断言函数,判断是否为真
 24     assert(w.shape == (dim,1))
 25     assert(isinstance(b,float) or isinstance(b,int))
 26     return(w,b)
 27 
 28 def propagate(w,b,X,Y):
 29     m = X.shape[1]
 30     #forward propagation
 31     A = sigmoid(np.dot(w.T,X) + b)
 32     cost = (-1./m)*np.sum(Y*np.log(A) + (1-Y)*np.log(1-A),axis = 1)#按行相加
 33     #backward propagation
 34     dw = (1./m)*np.dot(X,((A-Y).T))#dw就是损失函数对w的求导
 35     db = (1./m)*np.sum(A-Y, axis=1)#axis=0按列相加,axis=1按行相加
 36     assert(dw.shape == w.shape)
 37     assert(db.dtype == float)
 38     cost = np.squeeze(cost)#squeeze函数的作用是去掉维度为1的维,在这就是将一个一维变成一个数字
 39 #     [ 6.00006477]
 40 #     6.000064773192205
 41     assert(cost.shape == ())
 42     grads = {"dw": dw,
 43              "db": db}
 44     return grads, cost
 45 
 46 def optimize(w,b,X,Y,num_iterations,learning_rate,print_cost = False):
 47     costs = []
 48     for i in range(num_iterations):
 49         grads, cost = propagate(w=w, b=b, X=X, Y=Y)        
 50         dw = grads["dw"]
 51         db = grads["db"]   
 52         w = w - learning_rate*dw
 53         b = b -  learning_rate*db
 54         if i % 100 == 0:
 55             costs.append(cost)
 56         if print_cost and i % 100 == 0:#这句没懂
 57             print ("Cost after iteration %i: %f" %(i, cost))
 58     params = {"w": w,
 59               "b": b}
 60     grads = {"dw": dw,
 61              "db": db}
 62     return params, grads, costs
 63 
 64 def predict(w, b, X):
 65     m = X.shape[1]
 66     Y_prediction = np.zeros((1,m))
 67     w = w.reshape(X.shape[0], 1)   
 68     A = sigmoid(np.dot(w.T, X) + b)
 69 #     [print(x) for x in A]这句没懂,但对代码没啥影响
 70     for i in range(A.shape[1]):    
 71         if A[0, i] >= 0.5:
 72             Y_prediction[0, i] = 1    
 73         else:
 74             Y_prediction[0, i] = 0
 75     assert(Y_prediction.shape == (1, m))
 76     
 77     return Y_prediction
 78 
 79 def model(X_train, Y_train, X_test, Y_test, num_iterations = 2000, learning_rate = 0.5, print_cost = False):
 80     #初始化权值阈值
 81     w, b = initialiize_with_zeros(X_train.shape[0])
 82     #梯度下降法寻优获取最佳权值阈值
 83     parameters, grads, costs = optimize(w, b, X_train, Y_train, num_iterations, learning_rate, print_cost)
 84     w = parameters["w"]
 85     b = parameters["b"]
 86     #测试集进行预测
 87     Y_prediction_test = predict(w, b, X_test)
 88     Y_prediction_train = predict(w, b, X_train)
 89     #输出正确率
 90     print("train accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_train - Y_train)) * 100))
 91     print("test accuracy: {} %".format(100 - np.mean(np.abs(Y_prediction_test - Y_test)) * 100))
 92     #将所有结果以字典形式保存并返回
 93     d = {"costs": costs,
 94          "Y_prediction_test": Y_prediction_test, 
 95          "Y_prediction_train" : Y_prediction_train, 
 96          "w" : w, 
 97          "b" : b,
 98          "learning_rate" : learning_rate,
 99          "num_iterations": num_iterations}
100     
101     return d
102         
103 
104 
105 
106 \'\'\'主程序从这里开始\'\'\'
107 #获取训练数据,测试数据
108 train_set_x_orig, train_set_y, test_set_x_orig, test_set_y, classes = load_dataset()
109 
110 #reshape()方法来更改数组的形状,train_set_x_orig.shape[0]是行数,-1是代表列数未知,需要numpy自动计算出列数
111 #这里的列数:就是一张图片64*64*3数据变成一行数据的个数
112 train_set_x_flatten = train_set_x_orig.reshape(train_set_x_orig.shape[0], -1).T
113 test_set_x_flatten = test_set_x_orig.reshape(test_set_x_orig.shape[0], -1).T
114 
115 #归一,颜色的数值是0~255
116 train_set_x = train_set_x_flatten/255.
117 test_set_x = test_set_x_flatten/255.
118 
119 #训练模型
120 d = model(train_set_x, train_set_y, test_set_x, test_set_y, num_iterations = 2000, learning_rate = 0.005, print_cost = True)
121 print(d)

 

 


 
    
   


    

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